1998 Honda Accord timing belt

I have a 98 honda accord coupe that I have had for over a year. I was told to replace the timing belt at around 90,000 miles. Recently I have been experiencing problems with starting the engine. The problem has happened twice and is unreliable when or when it will not happen. When I turn the engine over, the engine does not fire up. I will wait for five minutes and usually the engine fires up. I drive the vehicle very well and am very cautious about keeping the car well maintained. Is the timing belt my problem? And if not, when should I replace my timing belt?